Wellposedness and convergence of solutions to a class of forced non-diffusive equations with applications

2019/02/28 by Susan Friedlander, Anthony Suen · 2 citations
Mathematics · #math.AP #msc:76D03 #msc:35Q35 #msc:76W05

paper · pdf · doi:10.1007/s00021-019-0454-1

arxiv created 2019/03/09 · arxiv updated 2019/10/02

Abstract

This paper considers a family of non-diffusive active scalar equations where a viscosity type parameter enters the equations via the constitutive law that relates the drift velocity with the scalar field. The resulting operator is smooth when the viscosity is present but singular when the viscosity is zero. We obtain Gevrey-class local well-posedness results and convergence of solutions as the viscosity vanishes. We apply our results to two examples that are derived from physical systems: firstly a model for magnetostrophic turbulence in the Earth's fluid core and secondly flow in a porous media with an "effective viscosity".

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